Unstable compositions related to the image of $J$
HTML articles powered by AMS MathViewer
- by Mark Mahowald and Robert Thompson PDF
- Proc. Amer. Math. Soc. 102 (1988), 431-436 Request permission
Abstract:
We study elements in the homotopy groups of spheres which are desuspensions of generators of the image of the $J$-homomorphism for $p = 2$. ${J_*}({\mathbf {R}}{P^\infty })$ is used to detect the nontriviality of compositions and Toda brackets involving these elements. Some formulas are derived which show how various compositions of these elements are related to one another.References
- J. F. Adams, On the groups $J(X)$. IV, Topology 5 (1966), 21β71. MR 198470, DOI 10.1016/0040-9383(66)90004-8
- Donald M. Davis and Mark Mahowald, $v_{1}$- and $v_{2}$-periodicity in stable homotopy theory, Amer. J. Math. 103 (1981), no.Β 4, 615β659. MR 623131, DOI 10.2307/2374044
- Mark Mahowald, The image of $J$ in the $EHP$ sequence, Ann. of Math. (2) 116 (1982), no.Β 1, 65β112. MR 662118, DOI 10.2307/2007048 β, Descriptive homotopy of the elements in the image of the $J$-homomorphism, Proc. Tokyo Conf. Manifolds, 1973, pp. 255-263.
- V. P. Snaith, A stable decomposition of $\Omega ^{n}S^{n}X$, J. London Math. Soc. (2) 7 (1974), 577β583. MR 339155, DOI 10.1112/jlms/s2-7.4.577
Additional Information
- © Copyright 1988 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 102 (1988), 431-436
- MSC: Primary 55Q40,; Secondary 55Q50
- DOI: https://doi.org/10.1090/S0002-9939-1988-0921012-X
- MathSciNet review: 921012